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Elements of Modern Algebra, by Jimmie Gilbert, Linda Gilbert
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Helping to make the study of modern algebra more accessible, this text gradually introduces and develops concepts through helpful features that provide guidance on the techniques of proof construction and logic analysis. The text develops mathematical maturity for students by presenting the material in a theorem-proof format, with definitions and major results easily located through a user-friendly format. The treatment is rigorous and self-contained, in keeping with the objectives of training the student in the techniques of algebra and of providing a bridge to higher-level mathematical courses.
- Sales Rank: #1345909 in Books
- Brand: Brand: Brooks Cole
- Published on: 2004-08-10
- Original language: English
- Number of items: 1
- Dimensions: .87" h x 7.58" w x 9.34" l, 1.10 pounds
- Binding: Hardcover
- 430 pages
- Used Book in Good Condition
About the Author
Jimmie Gilbert was Professor of Mathematics at the University of South Carolina, Upstate. He received his Ph.D from Auburn University with a specialty in Linear and Abstract Algebras. He authored the first edition of Elements of Modern Algebra in 1970, joined on subsequent editions by his wife and longtime co-author Linda Gilbert. Together they have published titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, Intermediate Algebra, and another Cengage Learning title, Linear Algebra and Matrix Theory, now in its second edition. He and Linda have 6 children and 8 grandchildren. In his leisure time Jimmie enjoyed the outdoors, fishing, and gardening.
Linda Gilbert received her Ph.D. from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband Jimmie Gilbert, including ELEMENTS OF MODERN ALGEBRA and LINEAR ALGEBRA and MATRIX THEORY (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra.
Most helpful customer reviews
13 of 14 people found the following review helpful.
thats how math books should be written!!! (but plz, change that price there)
By atwi_confidence
It is surely one of the books I most enjoyed!!
But its pricey, thats why a lot of colleges (or professors) try to avoid it.
The book has eight chapters:
1) Fundamentals
2) The integers
3) Groups
4) More on Groups
5) Rings, Integral domains, and fields
6) More on rings
7) Real and Complex Numbers
8) Ploynomials.
Definitions and Theorems stand out in Boxes, then later comes the examples!! (Plz Mathematicians who write books, just take a look here, see how nicely a book can be written, then go for the challenge).
one of the good things in this book, is that it does not assume you took a class in number theory before, so it introduces in the first two chapters everything (from a typical number theory class) that you would need in modern algebra class. (that might be a drawback for a student who took number theory class, and his professor is determined to start from the first chapter in this book).
other than the definitions and theorems stand out clearly, The author give examples on how that theorem can be used!! and The examples sometimes are really good!!
What's best in this book, are the problems after each chapter, they rank from direct applications to theorems, to CHallenging problems! (at least challenging for me). But note that some of the problems depend on each other! so if ur stuck on one problem, that means you might need to use a result from an earlier problem in the same chapter. its a drawback that the author does not say "use problem ... to solve this one", I think they assume that anyone solving the problems, is solving all of them in sequence, which what students SHOULD do. There is no way you can get a good grasp on the material in this book, unless you are a genius, or you solve ALL the problems after each chapter (at least a very good amount of them). I found best thing to do is try solving them in sequence, if you dont have time to solve all of them, then skip the ones that you REALLY think you can solve, and this way you can use the result later on.
I would recommend this book to anyone interested in modern (abstract) algebra! But I think a pre-requisite to self-study in this book is exposition to how to write proofs rigorously. (well sure thats the pre-requisite for any math course, but usually this subject is one of the first subjects studied in upper level math courses, and you better take another course that exposes you to how to write proofs, if your buying this book for self-study).
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